Question

In what ratio does the x-axis divide the join of A(2, -3) and B (5, 6)?

(a) 2 : 3 (b) 3 : 5 (c) 1 : 2 (d) 2 : 1

Answer 1

Let x-axis divides the line segment joining the points (2, –3) and (5,6) in the ratio k:1.

Then, by using section formula, the point at which x-axis intersects the line segment is given by

P = $(\frac{5k+2}{k+1},\frac{6k-3}{k+1})$

It is known as the y ordinate of any point on the x-axis is 0

$\frac{6k-3}{k+1}=0$

$6k-3=0$

$k=\frac{3}{6}=\frac{1}{2}$

Thus, x-axis divides the line segment joining the points (2, –3) and (5,6) in the ratio 1:2.